IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v118y2019icp122-133.html
   My bibliography  Save this article

The dynamics of viral infection in toxin producing phytoplankton and zooplankton system with time delay

Author

Listed:
  • Agnihotri, Kulbhushan
  • Kaur, Harpreet

Abstract

Dynamical behaviour of virally infected toxin producing phytoplankton and zooplankton system is explored with the assumption that toxin liberation is not an instantaneous process. It is further hypothesized that the infected phytoplankton species do recover from disease. It is established that time delay in toxin liberation process can destabilize the otherwise stable equilibrium state. The coexistence of all the species is observed through the periodic oscillations as a result of Hopf bifurcation. Normal form theory and central manifold arguments are applied to determine the direction of Hopf bifurcation and stability of bifurcating periodic orbits. Analytical results are supported with the help of numerical simulations.

Suggested Citation

  • Agnihotri, Kulbhushan & Kaur, Harpreet, 2019. "The dynamics of viral infection in toxin producing phytoplankton and zooplankton system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 122-133.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:122-133
    DOI: 10.1016/j.chaos.2018.11.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918303242
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.11.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Juneja, Nishant & Agnihotri, Kulbhushan & Kaur, Harpreet, 2018. "Effect of delay on globally stable prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 146-156.
    2. Nurul Huda Gazi & Malay Bandyopadhyay, 2006. "Effect of time delay on a detritus-based ecosystem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-28, October.
    3. Gakkhar, Sunita & Sahani, Saroj Kumar & Negi, Kuldeep, 2009. "Effects of seasonal growth on delayed prey–predator model," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 230-239.
    4. Das, Kalyan & Ray, Santanu, 2008. "Effect of delay on nutrient cycling in phytoplankton–zooplankton interactions in estuarine system," Ecological Modelling, Elsevier, vol. 215(1), pages 69-76.
    5. Karimi, Hamid Reza & Maass, Peter, 2009. "Delay-range-dependent exponential H∞ synchronization of a class of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1125-1135.
    6. Zhao, Jiantao & Wei, Junjie, 2009. "Stability and bifurcation in a two harmful phytoplankton–zooplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1395-1409.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Agnihotri, Kulbhushan & Kaur, Harpreet, 2021. "Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 946-964.
    2. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    3. Thakur, Nilesh Kumar & Ojha, Archana & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2021. "An investigation of delay induced stability transition in nutrient-plankton systems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thakur, Nilesh Kumar & Ojha, Archana & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2021. "An investigation of delay induced stability transition in nutrient-plankton systems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Jiang, Zhichao & Zhang, Tongqian, 2017. "Dynamical analysis of a reaction-diffusion phytoplankton-zooplankton system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 693-704.
    3. Shi, Renxiang & Yu, Jiang, 2017. "Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 62-73.
    4. Juneja, Nishant & Agnihotri, Kulbhushan, 2018. "Conservation of a predator species in SIS prey-predator system using optimal taxation policy," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 86-94.
    5. Feng-Hsiag Hsiao, 2016. "A neural-network-based exponential synchronisation for chaotic secure communication via improved genetic algorithm," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(13), pages 3149-3166, October.
    6. Feng-Hsiag Hsiao, 2017. "Optimal fuzzy control of exponential synchronisation via genetic algorithm," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(8), pages 1569-1580, June.
    7. Raw, Sharada Nandan & Sahu, Sevak Ram, 2023. "Strong stability with impact of maturation delay and diffusion on a toxin producing phytoplankton–zooplankton model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 547-570.
    8. Chuanjun Dai & Hengguo Yu & Qing Guo & He Liu & Qi Wang & Zengling Ma & Min Zhao, 2019. "Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    9. Barman, Binandita & Ghosh, Bapan, 2019. "Explicit impacts of harvesting in delayed predator-prey models," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 213-228.
    10. Renu, & Upadhyay, Ranjit Kumar & Tiwari, S.P. & Yadav, R.P., 2023. "Analysis of interval-valued model for interaction between plankton-fish population in marine ecosystem," Ecological Modelling, Elsevier, vol. 484(C).
    11. Li, Kai & Wei, Junjie, 2009. "Stability and Hopf bifurcation analysis of a prey–predator system with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2606-2613.
    12. Panja, Prabir & Mondal, Shyamal Kumar & Jana, Dipak Kumar, 2017. "Effects of toxicants on Phytoplankton-Zooplankton-Fish dynamics and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 389-399.
    13. Lu, Chun, 2022. "Dynamical analysis and numerical simulations on a crowley-Martin predator-prey model in stochastic environment," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    14. Soukaina, Ben Rhila & Imane, Agmour & Mostafa, Rachik & Naceur, Achtaich & Youssef, El Foutayeni, 2022. "Optimal control of a phytoplankton-zooplankton spatiotemporal discrete bioeconomic model," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    15. Poria, Swarup & Poria, Anindita Tarai & Chatterjee, Prasanta, 2009. "Synchronization threshold of a coupled n-dimensional time-delay system," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1123-1124.
    16. Karimi, Hamid Reza & Zapateiro, Mauricio & Luo, Ningsu, 2009. "Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 595-603.
    17. Agnihotri, Kulbhushan & Kaur, Harpreet, 2021. "Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 946-964.
    18. Zhang, Jia-Fang & Wang, Shaoli & Kong, Xiangjun, 2018. "Effects of toxin delay on the dynamics of a phytoplankton–zooplankton model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1150-1162.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:122-133. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.